Recently, in NMR, high-sensitive coils composed of multiple relatively high sensitive element RF coils that are called multiple or phased array coil (hereinafter, referred to as multiple coil) are in heavy usage as an RF coil receiving NMR signals. They can have a larger field of view (FOV) while keeping high sensitivity of element RF coil, and achieve higher sensitivity by synthesizing signals received by each element RF coil.
There is a method for shortening imaging time by the use of reduced number of measurement data by using such multiple coils. This method is called space encoding, parallel imaging or parallel MRI method, and is referred to as “parallel MRI” in this specification. In the parallel MRI, imaging is performed by reducing (thinning) the number of data in the phase encoding direction. And aliasing in image, which is generated due to the thinning of phase encoding data, can be prevented by using a sensitivity distribution of element RF coils different spatially from each other. The prevention of aliasing requires operation using a sensitivity distribution of high-precision RF coil. There are two methods, SMASH method and SENSE method. The SMASH method performs the operation in measurement space (k-space) and complements thinned out data by interpolation, while the SENSE method removes aliasing by performing the operation in a real space after Fourier transform.
As an MRI imaging methods, there is a method called Cartesian imaging, in which at the sampling of echo signals on the measurement space (namely the space called k-space) the sampling parallel to the frequency encoding direction (Kx axis on the k-space) is repeated along the phase encoding direction (Ky axis on the k-space). In Cartesian imaging, each sampling point is an orthogonal grid point that is intersection between the group of equally spaced lines parallel to the Kx axis and the group of equally spaced lines parallel to the Ky axis.
However, in the Cartesian imaging, when a subject is in motion while imaging is performed, such motion may exert an influence on the entire image and cause an artifact (hereinafter, referred to as “motion artifact”), which looks like a flowing of an image in the phase encoding direction. As an imaging method capable of preventing such artifacts, the method called non-Cartesian imaging is now under development for practical application. One of the typical non-Cartesian imaging methods is a radial scan or spiral scan. Since these non-Cartesian imaging methods radially scan the k-space, they sample the data on points (non-orthogonal grid points) other than orthogonal grid points that are sampling points in the above-mentioned Cartesian imaging.
There has been proposed to further speed-up such non-Cartesian imaging by applying the above-mentioned parallel MRI while preventing the occurrence of motion artifacts (Non-patent Document 1, Non-patent Document 2 and Patent Document 1). In non-Cartesian imaging, the artifacts produced when the data is roughly obtained by applying parallel MRI are more complicated than those produced in Cartesian imaging. In the SENSE method, these artifacts can be prevented by using a generalized parallel method.
As the generalized parallel method performs operations by assuming that aliasing artifacts enter into each point from all points (all pixels except itself) in a real space, it takes longer time to operate an increased amount of computation. Consequently, the generalized parallel method has disadvantages such as difficulty in high speed computation and lower practicality as it needs to compute a larger amount of computation, including recursive processing. In view of these, the SMASH method is now a mainstream of non-Cartesian parallel MRI presented at the ISMRM.
[Non-Patent Document 1]
    K P. Pruessmann et al (3). “Advances in sensitivity encoding with arbitrary k-space trajectories” Magnetic Resonance in Medicine 46, p. 638-651, (2001)[Non-Patent Document 2]    E N. Yeh, et al (8), “Inherently self-calibrating non-Cartesian parallel imaging” Magnetic Resonance in Medicine 54, p. 1-8, (2005)[Patent Document 1]    Japan Published unexamined patents application No. 2004-344183